KYIV, UKRAINE—Ukraine’s beleaguered president on Monday agreed to scrap harsh anti-protest laws that set off a wave of clashes between protesters and police over the past week.

Justice Minister Elena Lukash, in a statement on the presidential website, said that in a meeting on Monday night with top opposition figures and President Viktor Yanukovych, “a political decision was made on scrapping the laws of Jan. 16, which aroused much discussion.”

Yanukovych pushed those laws through parliament. Three days later clashes with police broke out, a sharp escalation of tensions after weeks of mostly peaceful protests.

Eliminating the laws, which is likely to be done in a special parliament session Tuesday, would be a substantial concession to the opposition. But it does not meet all their demands, which include Yanukovych’s resignation.

One of the opposition figures, Arseniy Yatsenyuk, turned down the prime minister’s job, which Yanukovych offered him on Saturday.

At that time, he said protests would continue. In the Monday meeting, Yanukovych said a proposed amnesty for arrested protesters would not be offered unless demonstrators stopped occupying buildings and ended their round-the-clock protests and tent camp on Kyiv’s central square.

Protesters have been afraid that authorities were preparing to end the spreading demonstrations by force, but the foreign ministry said earlier the government has no immediate plans to declare a state of emergency.

Three protesters died in the clashes last week, two of whom were shot by hunting rifles, which police insist they do not use. With protesters now willing to risk injury, a state of emergency would be likely to set off substantial fighting on the streets of the capital.

“Today, such a measure is not on the table,” Foreign Minister Leonid Kozhara told journalists.

EU foreign policy chief Catherine Ashton said in a statement that she was alarmed by reports about the government considering a state of emergency and warned that such a move “would trigger a further downward spiral for Ukraine which would benefit no one.”

The protesters still occupy three sizable buildings in downtown Kyiv, including City Hall. One of the buildings was seized in a spectacular assault early Sunday, when hundreds of protesters threw rocks and firebombs into the building where about 200 police were sheltering. The crowd eventually formed a corridor through which the police left.

Lukash, in a televised statement, noted that protesters seized the building as justice employees were working on measures to grant amnesty to protesters and to make changes in the constitution to restore more power to the prime minister.

It’s not clear if constitutional changes will be on the agenda for Tuesday’s parliamentary session, but granting more power to the prime minister could both sweeten the offer and allow Yanukovych to portray himself as offering genuine compromise.

The protests began in late November when Yanukovych shelved a long-awaited agreement to deepen ties with the 28-nation European Union and sought a bailout loan from Russia. The demonstrations grew in size and intensity after police violently dispersed two gatherings.